I was curious and was able to reproduce such a small window that keeps persistently that small.
In hindsight, alt-space would have been the better shortcut. You sure, you had the tiny window in focus? Was it dragable? Closeable with X? If not, maybe it was a different esoteric bug.
But the storage file for position is config.json in the itch folder in roaming. I thought there was a mechanism provided by the OS, but apparantly every app does it differently.
If you wonder how that could have happened, when the system tries to change to a resolution that does not work, the desktop sometimes gets resized as well and open windows try to resize if too big when the desktop is shrunk. And that download window does has a tiny minimum size. Other windows have bigger minimum size.
Edit: if it was not interactable, it was probably off-screen. alt-space and minimize and maximize would have worked. You can try this for fun now. Change the values in the config.json to something like this
"x":5000,"y":100,"width":50,"height":7